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Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
A Propositional Modal Logic of Time Intervals
 Journal of the ACM
, 1996
"... : In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end we develop a modal temporal logic based on time intervals, a logic which can be viewed as a gener ..."
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: In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end we develop a modal temporal logic based on time intervals, a logic which can be viewed as a generalization of pointbased modal temporal logic. We discuss related logics, give an intuitive presentation of the new logic, and define its formal syntax and semantics. We make no assumption about the underlying nature of time, allowing it to be discrete (such as the natural numbers) or continuous (such as the rationals or the reals), linear or branching, complete (such as the reals) or not (such as the rationals). We show, however, that there are formulas in the logic that allow us to distinguish all these situations. We also give a translation of our logic into firstorder logic, which allows us to apply some results on firstorder logic to our modal one. Finally, we consider the difficulty o...
METATEM: A Framework for Programming in Temporal Logic
 In REX Workshop on Stepwise Refinement of Distributed Systems: Models, Formalisms, Correctness (LNCS Volume 430
, 1989
"... In this paper we further develop the methodology of temporal logic as an executable imperative language, presented by Moszkowski [Mos86] and Gabbay [Gab87, Gab89] and present a concrete framework, called METATEM for executing (modal and) temporal logics. Our approach is illustrated by the developmen ..."
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Cited by 88 (19 self)
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In this paper we further develop the methodology of temporal logic as an executable imperative language, presented by Moszkowski [Mos86] and Gabbay [Gab87, Gab89] and present a concrete framework, called METATEM for executing (modal and) temporal logics. Our approach is illustrated by the development of an execution mechanism for a propositional temporal logic and for a restricted first order temporal logic.
Reasoning about Time in the Situation Calculus.
, 1995
"... We extend the ontology of the situation calculus to provide for the representation of time and event occurrences. We do this by defining a time line corresponding to a sequence of situations (called actual situations) beginning with the initial situation. Actual situations are totally ordered and ..."
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Cited by 41 (4 self)
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We extend the ontology of the situation calculus to provide for the representation of time and event occurrences. We do this by defining a time line corresponding to a sequence of situations (called actual situations) beginning with the initial situation. Actual situations are totally ordered and the actions that lead to different actual situations are said to have occurred. This exension to the situation calculus permits one to express truths about the state of the world at different times. For example, we can state that at some point in the future certain fluent will be true. We can also express constraints on the occurrences of events, for example, that after releasing a cup, it will eventually hit the floor. Our version of the situation calculus subsumes other temporal logics. In particular, we show that the modal Temporal Logic of Concurrency [4] can be embedded in the extended situation calculus. Our extension can also realize the essential features of other first ord...
Automated Temporal Reasoning about Reactive Systems
, 1996
"... . There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective a ..."
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Cited by 41 (2 self)
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. There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective and reliable means of specifying and ensuring correct behavior of such systems. This paper discusses known complexity and expressiveness results for a number of such logics in common use and describes key technical tools for obtaining essentially optimal mechanical reasoning algorithms. However, the emphasis is on underlying intuitions and broad themes rather than technical intricacies. 1 Introduction There is a growing need for reliable methods of designing correct reactive systems. These systems are characterized by ongoing, typically nonterminating and highly nondeterministic behavior. Examples include operating systems, network protocols, and air traffic control systems. There is w...
Hyperdocuments as Automata: Verification of Tracebased Browsing Properties by Model Checking
, 1997
"... As hypertext systems proliferate and as networks become more ubiquitous, an important problem is to determine how to provide hyperdocument interoperability. Instead of taking the approach of standardizing, and implementing, a large and complex set of browsing features gleaned from some "union&q ..."
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Cited by 33 (3 self)
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As hypertext systems proliferate and as networks become more ubiquitous, an important problem is to determine how to provide hyperdocument interoperability. Instead of taking the approach of standardizing, and implementing, a large and complex set of browsing features gleaned from some "union" of existing systems, we present an approach that allows each document to encode its own browsing semantics in the links of the hyperdocument. Any implementation offering the "follow link" operation can then simulate the intent of the author. The method requires a mental shift in how a hyperdocument is viewed abstractly. Instead of treating the links of a document as defining a static directed graph, they are thought of as defining an abstract program, termed the linksautomaton of the document. A branching temporal logic notation, termed HTL*, is introduced for specifying properties a document should exhibit during browsing. An automated program verification technique called model checking is ...
Hyperdocuments as Automata: Tracebased Browsing Property Verification
 In Proceedings of the 1992 European Conference on Hypertext (ECHT92: November 30December 4
, 1992
"... In many hypertext systems, meaningfully traversing a document depends on capabilities, features, and navigational aids that are part of the browser implementation. For example, if a reader browses to a node that has no out links, then backing up, or "warping" to the table of contents can a ..."
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Cited by 30 (10 self)
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In many hypertext systems, meaningfully traversing a document depends on capabilities, features, and navigational aids that are part of the browser implementation. For example, if a reader browses to a node that has no out links, then backing up, or "warping" to the table of contents can allow the browsing session to continue. If hyperdocuments are to become interchangeable among hypertext systems, rather than being readable only on the systems from which they are authored, one obvious but complex approach is to try and standardize on (most likely, very many) browsing features and behaviors, forming some standard union of the capabilities of current major implementations. This approach molds (or perhaps restricts) future systems, since new browsing "features" must then be worked into such a standard. An alternate approach, used in this paper, is to deemphasized browser features and emphasize inherent document structure with browsing semantics. An author should be able to create docume...
A Road Map of Interval Temporal Logics and Duration Calculi
, 2004
"... We survey main developments, results, and open problems on interval temporal logics and duration calculi. We present various formal systems studied in the literature and discuss their distinctive features, emphasizing on expressiveness, axiomatic systems, and (un)decidability results. ..."
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Cited by 26 (11 self)
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We survey main developments, results, and open problems on interval temporal logics and duration calculi. We present various formal systems studied in the literature and discuss their distinctive features, emphasizing on expressiveness, axiomatic systems, and (un)decidability results.
Decidable and undecidable fragments of Halpern and Shoham’s interval temporal logic: towards a complete classification
 In Proc. of the 15th Int. Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), volume 5330 of LNCS
, 2008
"... Abstract. Interval temporal logics are based on temporal structures where time intervals, rather than time instants, are the primitive ontological entities. They employ modal operators corresponding to various relations between intervals, known as Allen’s relations. Technically, validity in interv ..."
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Abstract. Interval temporal logics are based on temporal structures where time intervals, rather than time instants, are the primitive ontological entities. They employ modal operators corresponding to various relations between intervals, known as Allen’s relations. Technically, validity in interval temporal logics translates to dyadic secondorder logic, thus explaining their complex computational behavior. The full modal logic of Allen’s relations, called HS, has been proved to be undecidable by Halpern and Shoham under very weak assumptions on the class of interval structures, and this result was discouraging attempts for practical applications and further research in the field. A renewed interest has been recently stimulated by the discovery of interesting decidable fragments of HS. This paper contributes to the characterization of the boundary between decidability and undecidability of HS fragments. It summarizes known positive and negative results, it describes the main techniques applied so far in both directions, and it establishes a number of new undecidability results for relatively small fragments of HS. 1
Propositional Interval Neighborhood Logics: Expressiveness, Decidability, and Undecidable Extensions
"... In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics (PNL), we establish their decidability on linearly ordered domains and some important subclasses, and we prove undecidability of a number of extensions of PNL with additional modalities ov ..."
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Cited by 18 (10 self)
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In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics (PNL), we establish their decidability on linearly ordered domains and some important subclasses, and we prove undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal decidable fragment of HalpernShoham’s interval logic HS.